﻿On 
  Measuring 
  the 
  Torsional 
  Angle 
  of 
  a 
  Rotating 
  Shaft 
  fyc. 
  183 
  

  

  thus 
  the 
  energy 
  \mu* 
  communicated 
  to 
  the 
  ion 
  is 
  equal 
  to 
  

  

  1EW 
  

  

  2 
  V 
  2 
  ' 
  

  

  Now 
  the 
  energy 
  in 
  the 
  pulse 
  is 
  proportional 
  to 
  ffld/Y 
  2 
  , 
  so 
  

   that 
  the 
  ratio 
  of 
  the 
  energy 
  communicated 
  to 
  the 
  ion 
  to 
  the 
  

   energy 
  in 
  the 
  pulse 
  is 
  proportional 
  to 
  d. 
  Thus 
  the 
  broader 
  

   the 
  pulse, 
  the 
  greater 
  the 
  absorption 
  and 
  the 
  less 
  the 
  penetrat- 
  

   ing 
  power. 
  The 
  energy 
  in 
  the 
  pulse 
  is 
  inversely 
  proportional 
  

   to 
  its 
  thickness. 
  

  

  If 
  we 
  return 
  to 
  the 
  expression 
  for 
  the 
  intensity 
  of 
  the 
  mag- 
  

   netic 
  force 
  in 
  case 
  (1), 
  we 
  see 
  that 
  it 
  is 
  proportional 
  to 
  sin 
  6, 
  

   so 
  that 
  the 
  disturbance 
  is 
  greatest 
  at 
  right 
  angles 
  to 
  the 
  

   cathode 
  rays 
  : 
  thus, 
  if 
  the 
  cathode 
  particles 
  are 
  stopped 
  at 
  their 
  

   first 
  encounter, 
  the 
  Rontgen 
  rays 
  would 
  be 
  brightest 
  at 
  right 
  

   angles 
  to 
  the 
  cathode 
  rays; 
  if, 
  however, 
  as 
  would 
  seem 
  most 
  

   probable, 
  the 
  cathode 
  particles 
  had 
  to 
  make 
  several 
  encounters 
  

   before 
  they 
  were 
  reduced 
  to 
  rest, 
  changing 
  their 
  direction 
  

   between 
  each 
  encounter, 
  the 
  distribution 
  of 
  the 
  cathode 
  rays 
  

   would 
  be 
  much 
  more 
  uniform. 
  Experiments 
  on 
  the 
  distri- 
  

   bution 
  of 
  Rontgen 
  rays 
  produced 
  by 
  the 
  impact 
  of 
  the 
  cathode 
  

   particles 
  directly 
  against 
  the 
  walls 
  of 
  the 
  discharge-tube 
  are, 
  

   as 
  Sir 
  George 
  Stokes 
  has 
  pointed 
  out, 
  affected 
  by 
  the 
  much 
  

   greater 
  absorption 
  of 
  the 
  oblique 
  rays 
  produced 
  by 
  the 
  greater 
  

   thickness 
  of 
  glass 
  traversed 
  by 
  them. 
  Experiments 
  on 
  rays 
  

   produced 
  by 
  focus-tubes 
  would 
  give 
  results 
  more 
  easily 
  

   interpreted. 
  

  

  The 
  result 
  to 
  which 
  we 
  have 
  been 
  led 
  from 
  the 
  considera- 
  

   tion 
  of 
  the 
  effects 
  produced 
  by 
  the 
  sudden 
  stoppage 
  of 
  an 
  

   electrified 
  particle, 
  viz. 
  : 
  that 
  the 
  Rontgen 
  effects 
  are 
  produced 
  

   by 
  a 
  very 
  thin 
  pulse 
  of 
  intense 
  electromagnetic 
  disturbance, 
  is 
  

   in 
  agreement 
  with 
  the 
  view 
  expressed 
  by 
  Sir 
  George 
  Stokes 
  

   in 
  the 
  Wilde 
  Lecture 
  (' 
  Proceedings 
  of 
  Manchester 
  Literary 
  

   and 
  Philosophical 
  Society/ 
  1897), 
  that 
  the 
  Rontgen 
  rays 
  are 
  

   not 
  waves 
  of 
  very 
  short 
  wave-length, 
  but 
  impulses. 
  

  

  Cambridge, 
  

   Dec. 
  16, 
  1897. 
  

  

  XVIII. 
  A 
  New 
  Method 
  of 
  Measuring 
  the 
  Torsional 
  Angle 
  of 
  a 
  

   Rotating 
  Shaft 
  or 
  Spiral 
  Spring. 
  By 
  Frederick 
  J. 
  Jervis- 
  

   Smith, 
  M.A., 
  F.R.S., 
  Millard 
  and 
  University 
  Lecturer 
  in 
  

   Mechanics, 
  Oxford*. 
  

  

  WHEN 
  an 
  elastic 
  shaft 
  is 
  used 
  to 
  transmit 
  motion, 
  the 
  

   power 
  transmitted 
  can 
  be 
  found, 
  when 
  the 
  number 
  of 
  

   rotations 
  in 
  unit 
  time 
  and 
  the 
  torsional 
  couple 
  of 
  the 
  shaft 
  

   * 
  Communicated 
  by 
  the 
  Author. 
  

  

  